The Act of Creation

by Arthur Koestler

  These sub-skills of symbolic thought have been discussed in various contexts. They range from the implicit codes of grammar, syntax, and commonsense logic, through the operational rules of extrapolation, interpolation, transposition, schematization (exaggeration and simplification), and so forth, to the special rules of such special games as vector-analysis or biochemistry. But even these very special and complex skills can be practised by sheer routine; and vice versa some of the most original discoveries arose out of relatively simple problems. Complexity of thought is no measure of originality.

  Searching for a Code

  Polya defines a routine problem as one 'which can be solved either by substituting special data into a formerly solved general problem, or by following step by step, without any trace of originality, some well-worn, conspicuous example'. [2] He contrasts these routines with the 'rules of discovery': 'The first rule of discovery is to have brains and good luck. The second rule of discovery is to sit tight and wait till you get a bright idea.' [3] And he defines a 'bright idea' as 'a sudden leap of the imagination, a flash of genius'. [4]

  However, most practical and theoretical problems are solved at some level between these two extremes. Polya's definition of routine is too narrow and rigid; it does not take into account the great flexibility, for instance, of sensory-motor skills such as rock-climbing, or glass-blowing, or playing an instrument in an uninspired but technically accomplished manner. In symbolic thinking we find equally flexible skills which are nevertheless routine: solicitors dictating a document or brief; interpreters at public congresses dictating ad hoc into the multi-lingual earphone-circuits; politicians on whistle-stop tours reeling off variations on well-worn themes. These are routine performances in Polya's sense of 'substituting special data into general equations'; but the equation, the code, leaves in these cases many more degrees of freedom than does a mathematical formula, and the act of 'substituting special data' has varying degrees of trickiness. Even to a skilled and expert translator, for instance, it often happens that he has no ready-made idiom or turn of phrase in his repertory to substitute for the original. He must improvise some approximation, perhaps a metaphor, to cover the meaning -- which is a much higher skill, involving a degree of originality.

  Turning to more difficult problems, of the type which Duncker and Maier put to their subjects, we find routine solutions combined with intimations of originality, and we shall recognize an increasing number of those factors, in embryonic shape as it were, which we saw at work in the creative process.

  The degree of originality which a subject will display depends, ceteris paribus, on the nature of the challenge -- that is, the novelty and unexpectedness of the situation. Familiar situations are dealt with by habitual methods; they can be recognized, at a glance, as analogous in some essential respect to past experiences which provide a ready-made rule to cope with them. The more new features a task contains, the more difficult it will be to find the relevant analogy, and thereby the appropriate code to apply to it. We have seen (Book One, VIII, XVII) that one of the basic mechanisms of the Eureka process is the discovery of a hidden analogy; but 'hiddenness' is again a matter of degrees. How hidden is a hidden analogy, and where is it hidden? And what does the word 'search' mean in this context? In the terms of the present theory it means a process of scanning, of bringing successive, perceptual or conceptual analyser-codes to bear on the problem; to try out whether the problem will match this type of filter or that, as the oculist tries out a series of lenses in the frame before the client's eyes. Yet the word 'search', so often used in the context of problem-solving, is apt to create confusion because it implies that I know beforehand what I am searching for, whereas in fact I do not. If I search for a lost collar-stud, I put a kind of filter into my 'optical frame' which lets only collar-studs and similar shapes pass, and rejects everything else -- and then go looking through my drawers. But most tasks in problem-solving necessitate applying the reverse procedure: the subject looks for a clue, the nature of which he does not know, except that it should be a 'clue' (Ansatzpunkt, point d'appui), a link to a type of problem familiar to him. Instead of looking through a given filter-frame for an object which matches the filter, he must try out one frame after another to look at the object before 'his nose, until he finds the frame into which it fits, i.e. until the problem presents some familiar aspect -- which is then perceived as an analogy with past experience and allows him to come to grips with it.

  This search for the appropriate matrix, or rule of the game to tackle the process, is never quite random; the various types of guidance at the fumbling, groping, trying stages have been discussed before. Among the criteria which distinguish originality from routine are the level of consciousness on which the search is conducted, the type of guidance on which the subject relies, and the nature of the obstacle which he has to overcome.

  Degrees of Originality

  In one of Maier's ingenious experiments the problem set to the subject was to catch hold at the same time of two thin strings hung from the ceiling so wide apart that he could only get hold of one at a time. The only available tool was a pair of pliers. The solution is to tie the pliers to one string and set it into pendular motion. The crucial point of the experiment, however, is described as follows: [5]

  If the subject had not spontaneously solved the problem within ten minutes, Maier supplied him with a hint; he would "accidentally" brush against one of the strings, causing it to swing gently. Of those who solved the problem after this hint, the average interval between hint and solution was only forty-two seconds . . . . Most of those subjects who solved the problem immediately after the hint did so without any realization that they had been given one. The "idea" of making a pendulum with pliers seemed to arise spontaneously. (My italics.)

  Here we have a beautifully ambiguous example of what looks like 'unconscious' guidance. Obviously there is a world of difference between this kind of thing, and the nature of the sub-conscious processes which produce Kekulé's serpent dream or Poincaré's discovery of the Fuchsian functions. Maier's subjects seem to have 'cottoned on' to the solution on the pre-conscious or fringe-conscious level of awareness. Poincaré's inspiration was derived from the creative powers of the 'underground'.

  Nevertheless, we notice that while trivial tasks, in so far as they require any reflection at all, are solved in full daylight as it were, with the focus of awareness on the target, even problems of moderate difficulty, such as Maier's, require a type of guidance on a different level. Frequently the difficulty arises not from the objective novelty of the problem, but from its 'embeddedness' in the subject's mind. In Book One (p. 189) I have described an experiment of Duncker's in which an object was so embedded in its visible role as a 'pendulunl weight' that the student was unable to conceive of it in the role of a 'hammer'. 'Embeddedness' is a trivial version of the occasional 'snowblindness' of genius. In both cases the difficulty lies in going against routine -- in discarding the most obvious or likely matrix that offers itself and thus gets into the way of the more unlikely one which will do the job. But again there is more than a mere difference in degrees between overcoming the perceptual attachment of the weight to the string, and overcoming the millennial attachment of the human mind to the all-too-plausible axioms of Aristotelian physics.

  'Thinking aside' also occurs on all intermediate levels of difficulty. It may take the form of switching to visual imagery -- as in the problem of the Buddhist monk (Book One, p. 183); or of re-stating the problem in different terms; or letting one's attention wander, guided by some nascent, cloudy analogy. A good example is the Duncker-puzzle about the two trains and the bird. Two goods-trains, a hundred miles apart, start moving towards each other, each at a speed of twenty miles per hour. A silly bird, frightened by the starting hiss of one of the trains, flies away at thirty miles per hour in a straight line along the railway track until it meets the other train; it reverses its direction until it meets the first train, then turns again, and so forth. What distan
ce will the bird cover in its flight to and fro until the two trains meet?

  To compute the sum of the series of flight-stretches is a rather complicated task. But if we think aside, forget about the distances covered by the bird, and compute the time until the two trains will meet -- two and a half hours -- we see at once that the bird has also flown for two and a half hours and hence covered a total of seventy-five miles. The puzzle reflects in miniature Galileo's epocal discovery of the laws of free fall -- by switching his attention from the spatial 'to the temporal aspects of the process.

  Another famous Duncker problem is how to bring up exactly six pints of water from a river, when you have only two containers, one measuring nine, the other four pints. You fiddle around, decant in your imagination the big container twice into the smaller one, throwing the water each time back into the river. This leaves you with one pint which you can keep in the bigger or put into the smaller container -- but that does not help because now you cannot isolate the five pints to which the single pint must be added. The solution is simply to switch from addition to subtraction: you keep your pint in the smaller container, and fill it up from the larger one -- it will now only take 4 - 1 = 3 pints, leaving 9 - 3 = 6 pints in the large jug. Different people solve this problem by different methods. Polya gives an analytical explanation; personally I found that with most people the click occurs through the reversal of the direction of thought from addition to subtraction -- from figure to background -- a phenomenon we frequently met in discovery.

  At a certain level of problem-solving even a healthy kind of illogicality, of disregarding apparent contradictions, makes its appearance -- as in the image of the monk meeting his alter-ego. But enough has been said to show that as the challenge becomes more provoking, the nature of the guidance which directs the search for the right type of matrix to bear on the problem, becomes more intuitive, more remote from the normal routine of thinking, and that extra-conscious processes play an increasingly important part. And thus, having started from the base of the hierarchy, we arrive at last at the roof, which we have surveyed in the first volume but had left hanging in the air: the act of discovery.

  The term 'bisociation' is meant to point to the independent, autonomous character of the matrices which are brought into contact in the creative act, whereas associative thought operates among members of a single pre-existing matrix. But we have seen that this is a relative, not an absolute criterion, because the members of a matrix are sub-skills, i.e. matrices in their own right on a subordinate level of the hierarchy, and the degree of their integration, i.e. the coherence of the matrix, varies according to case. In matrices which have become fully automatized, the code alone determines which member shall act in which order -- the pedant always takes the same route to his office, his strategy is fixed once and for all, and has become incorporated into the code. But the more flexible a skill, the greater the part played by strategy. Thus in the problem about the trains and the bird, the subject must compute the distance D flown by the bird, and he knows that distances are computed by the rule of the game D = v.t. The velocity v of the bird is given, and he could get the t in a jiffy by substituting for it the time taken by the trains until they crash (t = 100/40 = 2½). Both the formula, and the process of substitution, are familiar sub-skills in the subject's repertory of habits, and should function as members of the matrix. However, owing to the unusual lie of the land -- i.e. the way the data are presented -- his strategy breaks down, the matrix goes to pieces, and its members function as independent entities. Once this has occurred it would require a certain originality to combine them again. We might even be generous and say, that to re-combine them would be a minor bisociative act.

  Thus the degree of independence of the matrices or submatrices which combine in the solution of a problem, can only be judged with reference to the subject's mental organization. Any boy of the sixth form can derive the Pythagorean theorem, which he has previously learned, as a matter of routine; but to discover it for himself would require a high degree of originality.

  I hope I have laid sufficient emphasis on the fact that originality must be measured on subjective scales and that any self-taught novelty is a minor bisociative act. This taken for granted, let me recapitulate the criteria which distinguish bisociative originality from associative routine.

  Association and Bisociation

  The first criterion was the previous independence of the mental skills or universes of discourse which are transformed and integrated into the novel synthesis of the creative act. The student solving the train-bird problem is entitled to shout Eureka because his mathematical skills are so poorly integrated (or so easily dislocated) that the act of 'hooking them together' appears to him a novel discovery. The more unlikely or 'far-fetched' the mediating matrix M2 -- i.e. the more independent from M1 -- the more unexpected and impressive the achievement. The creative act could be described as the highest form of learning because of the high improbability (or anti-chance probability) of the solution.

  If we now turn from subjective originality to discoveries which are new in actual fact, we again find the previous independence of the components that went into the 'good combination' to be a measure of achievement. Historically speaking, the frames of reference of magnetism and electricity, of physics and chemistry, of corpuscles and waves, developed separately and independently, both in the individual and the collective mind, until the frontiers broke down. And this breakdown was not caused by establishing gradual, tentative connections between individual members of the separate matrices, but by the amalgamation of two realms as wholes, and the integration of the laws of both realms into a unified code of greater universality. Multiple discoveries and priority disputes do not diminish the objective, historical novelty produced by these major bisociative events -- they merely prove that the time was ripe for that particular synthesis.

  Minor, subjective bisociative processes do occur on all levels, and are the main vehicle of untutored learning. But objective novelty comes into being only when subjective originality operates on the highest level of the hierarchies of existing knowledge.

  The discoveries of yesterday are the truisms of tomorrow, because we can add to our knowledge but cannot subtract from it. When two frames of reference have become integrated into one it becomes difficult to imagine that previously they existed separately. The synthesis looks deceptively self-evident, and does not betray the imaginative effort it needed to put its component parts together. In this respect the artist gets a better deal than the scientist. The changes of style in the representative arts, the discoveries which altered our frames of perception, stand out as great landmarks for all to see. The true creativity of the innovator in the arts is more dramatically evident and more easily distinguished from the routine of the mere practitioner than in the sciences, because art (and humour) operate primarily through the transitory juxtaposition of matrices, whereas science achieves their permanent integration into a cumulative and hierarchic order. Laurence Olivier in Hamlet is perceived as Olivier and as Hamlet at the same time; but when the curtain goes down, the two personae separate again, and do not become amalgamated into a higher unit which is later combined with others into still higher units.

  A further criterion of the creative act was that it involves several levels of consciousness. In problem-solving pre- and extra-conscious guidance makes itself increasingly felt as the difficulty increases; but in the truly creative act both in science and art, underground levels of the hierarchy which are normally inhibited in the waking state play a decisive part. It is perhaps significant that the German word for the Creator is "Schöpfer", and for creating "schöpfen" -- 'to scoop' in the sense of drawing water in buckets from a well. The Creator is thus visualized as creating the world out of His own depth, and the creative mind with a small c is supposed to apply a similar procedure. But whatever the inner sources on which the Lord of Genesis drew while his spirit hovered over the dark waters, in the case of humble mortals the sources are in t
he phylogenetically and ontogenetically older, underground layers of his mind. He can only reach them through a temporary regression to earlier, more primitive, less specialized levels of mentation, through a reculer pour mieux sauter. In this respect the creative act parallels the process of biological regeneration -- the liberation of genetic potentials normally under restraint, through the de-differentiation of damaged tissues. Thus the creative process involves levels of the mind separated by a much wider span than in any other mental activity -- except in pathological states, which represent a reculer sans sauter. The emotional manifestations of the Eureka act -- sudden illumination followed by abreaction and catharsis -- also testify to its subconscious origins; they are to some extent comparable to the cathartic effects of the analyst's method of bringing 'repressed complexes' into the patient's consciousness.

  The re-structuring of mental organization effected by the new discovery implies that the creative act has a revolutionary or destructive side. The path of history is strewn with its victims: the discarded isms of art, the epicycles and phlogistons of science.